The Hiremath Early Detection (HED) Score: A Measure-Theoretic Evaluation Standard for Temporal Intelligence

Researcher Prakul Hiremath has introduced the Hiremath Early Detection (HED) Score, a new measure-theoretic evaluation standard designed to quantify the time-value of information in systems monitoring non-stationary stochastic processes. The core innovation addresses a fundamental flaw in traditional evaluation paradigms like ROC/AUC, which treat early and late detections as equally valuable. In time-critical domains such as cybersecurity, surveillance, and epidemiology, this latency-agnostic approach is inadequate. The HED Score resolves this by integrating an exponentially decaying kernel over posterior probability streams, weighting detections that occur closer to the onset of a regime shift more heavily. The resulting scalar simultaneously encodes detection acuity, temporal lead, and pre-transition calibration quality.

Hiremath proves the HED Score satisfies three axiomatic requirements: Temporal Monotonicity, Invariance to Pre-Attack Bias, and Sensitivity Decomposability. The score is part of a parametric family indexed by the Hiremath Decay Constant (λ_H), with domain-specific calibrations forming the Hiremath Standard Table. As an empirical demonstration, Hiremath presents PARD-SSM (Probabilistic Anomaly and Regime Detection via Switching State-Space Models), which combines fractional Stochastic Differential Equations (fSDEs) with a Switching Linear Dynamical System inference backend. On the NSL-KDD cybersecurity benchmark, PARD-SSM achieved a HED Score of 0.0643, representing a 388.8% improvement over a Random Forest baseline (score 0.0132), with statistical significance confirmed via block-bootstrap resampling (p < 0.001). The paper positions the HED Score as the intended successor to ROC/AUC for evaluating temporal intelligence in predictive systems.